Publication number | US6997563 B1 |

Publication type | Grant |

Application number | US 10/849,998 |

Publication date | Feb 14, 2006 |

Filing date | May 19, 2004 |

Priority date | May 19, 2004 |

Fee status | Paid |

Also published as | US7175286, US7581839, US7850312, US20090268104 |

Publication number | 10849998, 849998, US 6997563 B1, US 6997563B1, US-B1-6997563, US6997563 B1, US6997563B1 |

Inventors | Zhongde Wang, Tianbing Brian Teng |

Original Assignee | Pixelworks, Inc. |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (9), Referenced by (62), Classifications (7), Legal Events (3) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US 6997563 B1

Abstract

A projector determines horizontal and vertical tilt angles. Using the tilt angles and the inherent properties of the projector, keystone correction corner points for the image can be computed. The keystone correction corner points can be used to perform keystone correction on the image.

Claims(56)

1. An apparatus, comprising:

an image projector to project an image;

a set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

a receiver to receive a vertical tilt angle βv and a horizontal tilt angle βh; and

a corrector to compute keystone correction corner points for the image using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times x-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{{d}^{6}}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),\mathrm{where}\phantom{\rule{0.8em}{0.8ex}}x\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}\phantom{\rule{0.8em}{0.8ex}}y$

represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

2. A projector according to claim 1 , wherein the receiver is operative to receive the vertical tilt angle βv and the horizontal tilt angle βh from a user.

3. A projector according to claim 1 , wherein the receiver is operative to determine the vertical tilt angle βv and the horizontal tilt angle βh relative to a surface.

4. A projector according to claim 1 , wherein the corrector performs keystone correction on the image using the keystone correction corner points for the image.

5. A projector according to claim 4 , wherein the corrector applies vertical scaling followed by horizontal scaling to the image to perform keystone correction.

6. A projector according to claim 4 , wherein the corrector applies horizontal scaling followed by vertical scaling to the image to perform keystone correction.

7. A projector according to claim 1 , wherein the receiver includes an adjuster to adjust the horizontal tilt angle βh based on the vertical tilt angle βv.

8. A projector, comprising:

means for projecting an image;

means for determining a set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

means for receiving a vertical tilt angle βv and a horizontal tilt angle βh; and

means for computing keystone correction corner points for the image using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times x-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{{d}^{6}}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),\mathrm{where}\phantom{\rule{0.8em}{0.8ex}}x\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}\phantom{\rule{0.8em}{0.8ex}}y$

represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

9. A projector according to claim 8 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for receiving the vertical tilt angle βv and the horizontal tilt angle βh from a user.

10. A projector according to claim 8 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for determining the vertical tilt angle βv and the horizontal tilt angle βh relative to a surface.

11. A projector according to claim 8 , further comprising means for performing keystone correction to the image using the keystone correction corner points for the image.

12. A projector according to claim 11 , wherein the means for performing keystone correction includes means for performing vertical scaling followed by horizontal scaling to the image to perform keystone correction.

13. A projector according to claim 11 , wherein the means for performing keystone correction includes means for performing horizontal scaling followed by vertical scaling to the image to perform keystone correction.

14. A projector according to claim 8 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

15. A method for performing keystone correction in a projector, comprising:

determining a set of inherent parameters for the projector, the set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

determining a vertical tilt angle βv;

determining a horizontal tilt angle βh; and

computing keystone correction corner points using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times x-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{{d}^{6}}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),\mathrm{where}\phantom{\rule{0.8em}{0.8ex}}x\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}\phantom{\rule{0.8em}{0.8ex}}y$

represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

16. A method according to claim 15 , further comprising performing keystone correction using the keystone correction corner points.

17. A method according to claim 16 , wherein performing keystone correction includes performing vertical scaling followed by horizontal scaling.

18. A method according to claim 16 , wherein performing keystone correction includes performing horizontal scaling followed by vertical scaling.

19. A method according to claim 15 , wherein determining a horizontal tilt angle βh includes adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

20. A method according to claim 15 , wherein determining a vertical tilt angle βv includes receiving the vertical tilt angle βv as an input from a user.

21. A method according to claim 15 , wherein determining a horizontal tilt angle βh includes receiving the horizontal tilt angle βh as an input from a user.

22. An article comprising a machine-accessible media having associated data, wherein the data, when accessed, results in a machine performing:

determining a set of inherent parameters for the projector, the set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

determining a vertical tilt angle βv;

determining a horizontal tilt angle βh; and

computing keystone correction corner points using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times x-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x}{{d}^{6}}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),\mathrm{where}\phantom{\rule{0.8em}{0.8ex}}x\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}\phantom{\rule{0.8em}{0.8ex}}y$

represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

23. An article according to claim 22 , the machine-accessible data further including associated data that, when accessed, results in performing keystone correction using the keystone correction corner points.

24. An article according to claim 23 , wherein performing keystone correction includes performing vertical scaling followed by horizontal scaling.

25. An article according to claim 23 , wherein performing keystone correction includes performing horizontal scaling followed by vertical scaling.

26. An article according to claim 22 , wherein determining a horizontal tilt angle βh includes adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

27. An article according to claim 22 , wherein determining a vertical tilt angle βv includes receiving the vertical tilt angle βv as an input from a user.

28. An article according to claim 22 , wherein determining a horizontal tilt angle βh includes receiving the horizontal tilt angle βh as an input from a user.

29. An apparatus, comprising:

an image projector to project an image; a set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

a receiver to receive a vertical tilt angle βv and a horizontal tilt angle βh; and

a corrector to compute keystone correction corner points for the image using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),$

where x and y represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

30. A projector according to claim 29 , wherein the receiver is operative to receive the vertical tilt angle βv and the horizontal tilt angle βh from a user.

31. A projector according to claim 29 , wherein the receiver is operative to receive the vertical tilt angle βv and the horizontal tilt angle βh relative to a surface.

32. A projector according to claim 29 , wherein the corrector performs keystone correction on the image using the keystone correction corner points for the image.

33. A projector according to claim 32 , wherein the corrector applies vertical scaling followed by horizontal scaling to the image to perform keystone correction.

34. A projector according to claim 32 , wherein the corrector applies horizontal scaling followed by vertical scaling to the image to perform keystone correction.

35. A projector according to claim 29 , wherein the receiver includes an adjuster to adjust the horizontal tilt angle βh based on the vertical tilt angle βv.

36. A projector, comprising:

means for projecting an image;

means for determining a set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

means for receiving a vertical tilt angle βv and a horizontal tilt angle βh; and

means for computing keystone correction corner points for the image using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),$

where x and y represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

37. A projector according to claim 36 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for receiving the vertical tilt angle βv and the horizontal tilt angle βh from a user.

38. A projector according to claim 36 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for determining the vertical tilt angle βv and the horizontal tilt angle βh relative to a surface.

39. A projector according to claim 36 , further comprising means for performing keystone correction to the image using the keystone correction corner points for the image.

40. A projector according to claim 39 , wherein the means for performing keystone correction includes means for performing vertical scaling followed by horizontal scaling to the image to perform keystone correction.

41. A projector according to claim 39 , wherein the means for performing keystone correction includes means for performing horizontal scaling followed by vertical scaling to the image to perform keystone correction.

42. A projector according to claim 36 , wherein the means for receiving a vertical tilt angle βv and a horizontal tilt angle βh includes means for adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

43. A method for performing keystone correction in a projector, comprising:

determining a set of inherent parameters for the projector, the set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

determining a vertical tilt angle βv;

determining a horizontal tilt angle βh; and

computing keystone correction corner points using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),$

where x and y represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

44. A method according to claim 43 , further comprising performing keystone correction using the keystone correction corner points.

45. A method according to claim 44 , wherein performing keystone correction includes performing vertical scaling followed by horizontal scaling.

46. A method according to claim 44 , wherein performing keystone correction includes performing horizontal scaling followed by vertical scaling.

47. A method according to claim 43 , wherein determining a horizontal tilt angle βh includes adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

48. A method according to claim 43 , wherein determining a vertical tilt angle βv includes receiving the vertical tilt angle βv as an input from a user.

49. A method according to claim 43 , wherein determining a horizontal tilt angle βh includes receiving the horizontal tilt angle βh as an input from a user.

50. An article comprising a machine-accessible media having associated data, wherein the data, when accessed, results in a machine performing:
where x and y represent an uncorrected pixel location and xp and yp represent a corrected pixel location.

determining a set of inherent parameters for a projector, the set of inherent parameters including a horizontal resolution Wn_{0}, a vertical resolution Hn_{0}, a depth d, and a vertical offset db;

determining a vertical tilt angle βv;

determining a horizontal tilt angle βh; and

computing keystone correction corner points using the set of inherent parameters, the vertical tilt angle βv, and the horizontal tilt angle βh using formulae
$\mathrm{xp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x-\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}\phantom{\rule{0.8em}{0.8ex}}\mathrm{and}$
$\mathrm{yp}\left[x,y\right]=\frac{\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y-\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right)}{1+\frac{\mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times x+\mathrm{cos}\left[\beta \phantom{\rule{0.3em}{0.3ex}}h\right]\times \mathrm{sin}\left[\beta \phantom{\rule{0.3em}{0.3ex}}v\right]\times y}{d}}+\left(\mathrm{db}-\frac{{\mathrm{Hn}}_{0}}{2}\right),$

51. An article according to claim 50 , the machine-accessible data further including associated data that, when accessed, results in performing keystone correction using the keystone correction corner points.

52. An article according to claim 51 , wherein performing keystone correction includes performing vertical scaling followed by horizontal scaling.

53. An article according to claim 51 , wherein performing keystone correction includes performing horizontal scaling followed by vertical scaling.

54. An article according to claim 50 , wherein determining a horizontal tilt angle βh includes adjusting the horizontal tilt angle βh based on the vertical tilt angle βv.

55. An article according to claim 50 , wherein determining a vertical tilt angle βv includes receiving the vertical tilt angle βv as an input from a user.

56. An article according to claim 50 , wherein determining a horizontal tilt angle βh includes receiving the horizontal tilt angle βh as an input from a user.

Description

This invention pertains to projectors, and more particularly to correcting distortion in a projected image.

Projectors have been around for quite some time. Historically, they projected only static images. The image to be projected would be placed a horizontal surface above a light source. Mirrors would then reflect the image onto a vertical surface parallel to the front of the projector, for easy viewing. The image could be raised or lowered by changing the angle of the mirror, and could be focused by raising or lowering the mirror (thereby changing the focal length of the projector).

With the advent of computers, manufacturers realized that projectors might be able to project dynamic (that is, changing) images. The first ventures in this area relied separate boxes that were placed on top of the light source, where the static images would have been placed. The computer was then responsible for changing the image in the box; the projector would show dynamic images by virtue of its light and mirror system.

Eventually, projector manufacturers realized that the two pieces could be combined. The projectors could connect directly to the computer and place the dynamic images directly in front of the light source, without requiring separate equipment. Projectors eventually moved from indirect (that is, reflected) projection systems to direct projection systems, where the image is oriented vertically, in a plane parallel to the projection surface.

But all of these systems suffered from a common problem. They all expect that the image, as projected, will be shown on a surface that is parallel to the front face of the projector. If the surface onto which the image is projected is not parallel to the front face of the projector, the image is distorted.

Various improvements to projectors have been made, to attempt to address this problem. For example, U.S. Pat. Nos. 6,520,547, 6,367,933, 6,305,805, and 6,339,434 each attempt to solve the problem. But each of these patents fails to completely solve the problem. U.S. Pat. No. 6,520,547, which uses 3×3 rotation matrices, does not work in a digital environment. U.S. Pat. No. 6,367,933 assumes that the optical axis of the projector is centered relative to the projected image, which is not usually the case. U.S. Pat. No. 6,305,805 warps the image by adding or deleting pixels, which is not an acceptable practice. And U.S. Pat. No. 6,337,434 only describes a scaling system in general.

Accordingly, a need remains for a way to correct for image distortion that addresses these and other problems associated with the prior art.

**105** is shown projecting image **110**. Image **110** is projected onto a surface (not shown). Under ideal circumstances, image **110** is projected onto the projection surface in such a way that, without correction, image **110** is perfectly rectangular. A coordinate system can be superimposed in the space, with the image in the XY-plane and projector **105** along the Z-axis, as shown in

In a preferred embodiment, the coordinate axes are positioned so that the Y-axis divides image **110** into two equal portions. That is, half of image **110** is to the left of the Y-axis, and half of image **110** is to the right of the Y-axis. But a person skilled in the art will recognize that this is not required, and that the image can be projected in a different spatial position than that shown in **110** still lying in the XY-plane).

Projector **105** projects images that have a width and height. A person skilled in the art will recognize that the projected images can be resized by moving projector **105** closer to (or further from) the projection surface (with possibly some refocusing of the projected image). When the projected image is so enlarged or shrunk, it is scaled: that is, everything grows or shrinks proportionately.

When projector **105** is positioned a specific distance d along the Z-axis, image **110** has a width Wn_{0 }and a height Hn_{0}. d, Wn_{0}, and Hn_{0 }are three inherent parameters of projector **105**. Under these circumstances, image **110** is said to be in nominal position. Note that, as mentioned above, projector **105** can be moved along the Z-axis, increasing or decreasing the distance d and changing the dimensions of image **110**. Mathematically, for any other distance d_{1}, the dimensions of image **110** can be computed, and these alternative values for d, Wn_{0}, and Hn_{0 }could be used.

The fourth parameter of projector **105** is db. db measures the distance from the NPL to the bottom of image **110**. Although **110** somewhere inside image **110**, a person skilled in the art will recognize that this is not required. That is, NPL could intersect the XY-plane outside image **110**: for example, below image **110** or above image **110**.

**105** is shown undergoing rotation through the horizontal plane (not shown in **105** is being rotated through the horizontal plane a horizontal tilt angle βh. Similarly, projector **105** is being rotated through a vertical plane (specifically, the YZ-plane) through a vertical tilt angle βv.

**105** has been rotated through an angle βh in the horizontal plane relative to projection surface **305**. As can been seen, the axis of projection of projector **105** is no longer normal to projection surface **305**. As a result, the image projected on projection surface **305** will be deformed. The right side of projection surface **305** will be closer to projector **105** than the left side of projection surface **305**.

**310**. Buttons **310** can be used to receive input from a user of projector **105**. For example, buttons **310** can be used to receive the tilt angle from the user. Although **310** positioned on the top of projector **105**, a person skilled in the art will recognize the buttons **310** can be positioned in other locations on projector **105**, and even disconnected from projector **105**: for example, on a remote controlled (not pictured). Buttons **310** are discussed further with reference to

Similar to **105** has been rotated through the vertical YZ-plane, so that it is angled relative to projection surface **305**. The image will be deformed, with the bottom of projection surface **305** closer to projector **105** than the top of projection surface **305**.

**105** has projection point **405**, which is the point within projector **105** from which the projection emanates. In **105**, is rotated relative to projection surface **305**. This image would be image **410**. As should be apparent, the horizontal and vertical tilt angles of image **410** are the same as the horizontal and vertical tilt angles of projector **105**: the difference is simply which frame of orientation is used.

To perform keystone correction, projector **105** uses corrector **415**. Understanding how corrector **415** performs keystone correction requires starting with the basic formulae for rotation. Mathematically, rotation through a horizontal tilt angle βh in the horizontal XZ-plane changes a vector

to a new vector

according to a simple formula:

Similarly, rotation through a vertical tilt angle βv produces the equation

Using the above-described rotation matrices, the deformation of the projected image can be computed, to describe image **410**. Note that image **410** is not necessarily (and in fact, unlikely to be) in the same plane as projection surface **305**: image **410** simply represents the result of rotating the nominal image through the horizontal and vertical tilt angles.

Next, lines are established between the four corners of the image **410** and projection point **405**. The intersection of these lines and projection surface **305** then defines the desired corners for image **420**. The projected image is then (internally to projector **105**) scaled so that the projected image fits within the established corners of image **420**. This deformed image, when projected onto projection surface **305**, then shows an undistorted image.

The procedure described with reference to

The reader might be wondering why there are two different sets of equations provided, when both rely on the same inputs (the inherent parameters of the projector, and the horizontal and vertical tilt angles βh and βv). The reason for the two sets of equations lies in the fact that not all projectors accomplish rotations the same ways. The difference between the two equation sets lies in how the term “horizontal plane” is defined.

As shown in

In case the above description was confusing, consider the following. Some projectors achieve rotation by elevating the front end of the projector: either using extendible legs, or by propping the projector, perhaps using books. This elevation accomplishes rotation through the vertical YZ-plane. To achieve rotation through the horizontal plane, the projector (along with any elevating materials) is swiveled on the table (or whatever surface the projector is resting on). In other words, the horizontal rotation is in the original XZ-plane, which was orthogonal to the projection surface. In this situation, Equation Set 1 is used.

But some projectors using a platform that can both rotate left and right and swivel up and down. Such a projector is not performing rotation in the original XZ-plane: instead, it is rotating horizontally in a tilted plane. Thus, to determine the “true” horizontal rotation (relative to the original XZ-plane) requires compensating for the fact that the projector has also been tilted vertically. In this situation, Equation Set 2 is used.

A person skilled in the art will recognize that, in fact, two equation sets are not needed. For projectors that rotate in the tilted XZ-plane, it is possible to mathematically adjust the horizontal tilt angle βh based on the vertical tilt angle βv. Then, Equation Set 1 can be used.

Once the correct equations to use have been determined (the correct equations are determined by the physical structure of the projector, and can be determined at the time of manufacture), it is a simple matter to input to the equations the coordinates of the original corner points of the image and compute the keystone correction corner points. At this point, the image can be scaled as needed to produce an undistorted image on the projection surface. The procedure by which the image is scaled is generally beyond the scope of this document, but any scaling approach compatible with keystone correction can be used.

Although the inherent parameters of projector **105** are known in advance, the horizontal and vertical tilt angles depend on the specific use of projector **105**. Thus, the horizontal and vertical tilt angles βh and βv need to be determined somehow by projector **105**. The most common way for projector **105** to be informed of the horizontal and vertical tilt angles is by having the user press buttons (for example, buttons **310**) on projector **105**. With each button press, one of the horizontal or vertical tilt angles is slightly adjusted and the keystone correction performed anew. The user can press the up and down buttons to adjust the vertical tilt angle, and can press the left and right buttons to adjust the horizontal tilt angle. The user then views the result on projection surface **305** and adjusts changes the horizontal and vertical tilt angles again, if necessary.

But there are other ways to let projector **105** know the horizontal and vertical tilt angles. For example, the user could use a keypad to enter numerical values for the angles (this assumes the user can accurately measure the angles). Or, projector **105** could determine the angles directly, perhaps using gyroscopes. For example, the user could position projector **105** in the XZ-plane, let projector **105** know it is in the initial position (perhaps by pressing a button), then rotate projector **105** into its desired position. Such a system could also account for translational movement (that is, moving projector **105** to a different location in the coordinate system). For example, if projector **105** cannot be positioned properly initially in its final location (this can occur if the final position of projector **105** is not in the XZ-plane), projector **105** can be initially positioned in one location and then relocated to its final position. Projector **105** can then determine not only its rotation but also its translational movement (accounting for translation merely requires adding or subtracting values to x, y, and/or z before performing the rest of the computation). A person skilled in the art will recognize other ways in which projector **105** can determine its horizontal and vertical tilt angles.

**505**, the inherent properties of the projector are determined. At step **510**, the model of the projector is determined, so that the appropriate equation set can be applied. (In practice, the appropriate equation set is programmed in to the projector, so no actual determination is needed.) At step **515**, the vertical tilt angle βv is determined. At step **520**, the horizontal tilt angle βh is determined. If the horizontal tilt angle is affected by the vertical tilt angle, then at step **525** the horizontal tilt angle βh can be adjusted based on the vertical tilt angle βv. As shown by arrow **530**, step **525** is optional, and can be omitted. At step **535**, the projector computes the keystone correction corner points, using the formulae discussed above.

At step **540** (**545** the image is scaled vertically, then at step **550** the image is scaled horizontally. In another variation, at step **555** the image is scaled horizontally, then at step **560** the image is scaled vertically.

The following discussion is intended to provide a brief, general description of a suitable machine (i.e., projector) in which certain aspects of the invention may be implemented. Typically, the machine includes a system bus to which is attached processors, memory, e.g., random access memory (RAM), read-only memory (ROM), or other state preserving medium, storage devices, a video interface, and input/output interface ports. The machine may be controlled, at least in part, by input from conventional input devices, such as keyboards, mice, etc., as well as by directives received from another machine, interaction with a virtual reality (VR) environment, biometric feedback, or other input signal.

The machine may include embedded controllers, such as programmable or non-programmable logic devices or arrays, Application Specific Integrated Circuits, embedded computers, smart cards, and the like. The machine may utilize one or more connections to one or more remote machines, such as through a network interface, modem, or other communicative coupling. Machines may be interconnected by a way of a physical and/or logical network, such as an intranet, the Internet, local area networks, wide area networks, etc. One skilled in the art will appreciated that network communication may utilize various wired and/or wireless short range or long range carriers and protocols, including radio frequency (RF), satellite, microwave, Institute of Electrical and Electronics Engineers (IEEE) 802.11, Bluetooth, optical, infrared, cable, laser, etc.

The invention may be described by reference to or in conjunction with associated data including functions, procedures, data structures, application programs, etc. which when accessed by a machine results in the machine performing tasks or defining abstract data types or low-level hardware contexts. Associated data may be stored in, for example, the volatile and/or non-volatile memory, e.g., RAM, ROM, etc., or in other storage devices and their associated storage media, including hard-drives, floppy-disks, optical storage, tapes, flash memory, memory sticks, digital video disks, biological storage, etc. Associated data may be delivered over transmission environments, including the physical and/or logical network, in the form of packets, serial data, parallel data, propagated signals, etc., and may be used in a compressed or encrypted format. Associated data may be used in a distributed environment, and stored locally and/or remotely for machine access.

Having described and illustrated the principles of the invention with reference to illustrated embodiments, it will be recognized that the illustrated embodiments may be modified in arrangement and detail without departing from such principles. And although the foregoing discussion has focused on particular embodiments, other configurations are contemplated. In particular, even though expressions such as “according to an embodiment of the invention” or the like are used herein, these phrases are meant to generally reference embodiment possibilities, and are not intended to limit the invention to particular embodiment configurations. As used herein, these terms may reference the same or different embodiments that are combinable into other embodiments.

Consequently, in view of the wide variety of permutations to the embodiments described herein, this detailed description and accompanying material is intended to be illustrative only, and should not be taken as limiting the scope of the invention. What is claimed as the invention, therefore, is all such modifications as may come within the scope and spirit of the following claims and equivalents thereto.

Patent Citations

Cited Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US6305805 | Dec 17, 1998 | Oct 23, 2001 | Gateway, Inc. | System, method and software for correcting keystoning of a projected image |

US6339434 | Nov 23, 1998 | Jan 15, 2002 | Pixelworks | Image scaling circuit for fixed pixed resolution display |

US6367933 | Oct 1, 1999 | Apr 9, 2002 | Macronix International Co., Ltd. | Method and apparatus for preventing keystone distortion |

US6520547 | Jan 31, 2002 | Feb 18, 2003 | Phoenix Geometrix, Llc | Quick locking pipe joint for plain or profiled pipe |

US6592228 * | Dec 24, 1999 | Jul 15, 2003 | Matsushita Electric Industrial Co., Ltd | Projector comprising a microcomputer for controlling zoom and focus adjustments utilizing pattern generation and calculation means |

US6611260 | May 17, 1999 | Aug 26, 2003 | Pixelworks, Inc | Ultra-high bandwidth multi-port memory system for image scaling applications |

US6686973 * | Nov 30, 2000 | Feb 3, 2004 | Delta Electronics, Inc. | Method and apparatus for automatically correcting projection display of projector |

US6846081 * | Jul 18, 2003 | Jan 25, 2005 | Nec Viewtechnology, Ltd. | Projector |

US20040036844 * | Jun 12, 2003 | Feb 26, 2004 | Wood John S. | Automatic keystone correction system and method |

Referenced by

Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US7175286 * | Nov 30, 2005 | Feb 13, 2007 | Pixelworks, Inc. | Keystone correction derived from the parameters of projectors |

US7399086 * | Sep 8, 2005 | Jul 15, 2008 | Jan Huewel | Image processing method and image processing device |

US7441906 | Jul 5, 2005 | Oct 28, 2008 | Pixelworks, Inc. | Keystone correction system and method |

US7581839 | Jan 4, 2007 | Sep 1, 2009 | Pixelworks, Inc. | Keystone correction derived from the parameters of projectors |

US7705862 | Sep 15, 2006 | Apr 27, 2010 | Pixelworks, Inc. | System and method for improved keystone correction |

US7850312 | Jul 9, 2009 | Dec 14, 2010 | Pixelworks, Inc. | Keystone correction derived from the parameters of projectors |

US8376558 | Jun 30, 2008 | Feb 19, 2013 | The Invention Science Fund I, Llc | Systems and methods for projecting in response to position change of a projection surface |

US8384005 | Jul 11, 2008 | Feb 26, 2013 | The Invention Science Fund I, Llc | Systems and methods for selectively projecting information in response to at least one specified motion associated with pressure applied to at least one projection surface |

US8403501 | Jun 30, 2008 | Mar 26, 2013 | The Invention Science Fund, I, LLC | Motion responsive devices and systems |

US8430515 | Jun 30, 2008 | Apr 30, 2013 | The Invention Science Fund I, Llc | Systems and methods for projecting |

US8540381 | Jun 30, 2008 | Sep 24, 2013 | The Invention Science Fund I, Llc | Systems and methods for receiving information associated with projecting |

US8602564 | Aug 22, 2008 | Dec 10, 2013 | The Invention Science Fund I, Llc | Methods and systems for projecting in response to position |

US8608321 | Jun 30, 2008 | Dec 17, 2013 | The Invention Science Fund I, Llc | Systems and methods for projecting in response to conformation |

US8641203 | Jul 28, 2008 | Feb 4, 2014 | The Invention Science Fund I, Llc | Methods and systems for receiving and transmitting signals between server and projector apparatuses |

US8723787 | May 12, 2009 | May 13, 2014 | The Invention Science Fund I, Llc | Methods and systems related to an image capture projection surface |

US8733952 | Feb 27, 2009 | May 27, 2014 | The Invention Science Fund I, Llc | Methods and systems for coordinated use of two or more user responsive projectors |

US8820939 | Sep 30, 2008 | Sep 2, 2014 | The Invention Science Fund I, Llc | Projection associated methods and systems |

US8857999 | Aug 22, 2008 | Oct 14, 2014 | The Invention Science Fund I, Llc | Projection in response to conformation |

US8936367 | Jul 11, 2008 | Jan 20, 2015 | The Invention Science Fund I, Llc | Systems and methods associated with projecting in response to conformation |

US8939586 | Jul 11, 2008 | Jan 27, 2015 | The Invention Science Fund I, Llc | Systems and methods for projecting in response to position |

US8944608 | Jul 11, 2008 | Feb 3, 2015 | The Invention Science Fund I, Llc | Systems and methods associated with projecting in response to conformation |

US8955984 | Sep 30, 2008 | Feb 17, 2015 | The Invention Science Fund I, Llc | Projection associated methods and systems |

US9140974 | Aug 12, 2010 | Sep 22, 2015 | Thomson Licensing | Method and system for crosstalk and distortion corrections for three-dimensional (3D) projection |

US9143748 | Jul 1, 2010 | Sep 22, 2015 | Thomson Licensing | Method and system for differential distortion correction for three-dimensional (3D) projection |

US20060050243 * | Sep 8, 2005 | Mar 9, 2006 | Jan Huewel | Image processing method and image processing device |

US20070263181 * | Jan 21, 2005 | Nov 15, 2007 | Ben Q Mobile Gmbh & Co.Ohg | Method for Operating a Mobile Device for Projecting Image Data, and Mobile Projector Device |

US20090268104 * | Jul 9, 2009 | Oct 29, 2009 | Pixelworks, Inc. | Keystone correction derived from the parameters of projectors |

US20090309718 * | Jul 11, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods associated with projecting in response to conformation |

US20090309826 * | Jun 17, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and devices |

US20090309828 * | Feb 5, 2009 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for transmitting instructions associated with user parameter responsive projection |

US20090310035 * | Jul 28, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for receiving and transmitting signals associated with projection |

US20090310036 * | Aug 22, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for projecting in response to position |

US20090310037 * | Aug 22, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for projecting in response to position |

US20090310038 * | Aug 22, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Projection in response to position |

US20090310039 * | Jan 27, 2009 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for user parameter responsive projection |

US20090310088 * | Jun 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods for projecting |

US20090310089 * | Jun 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods for receiving information associated with projecting |

US20090310093 * | Jun 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods for projecting in response to conformation |

US20090310094 * | Jul 11, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods for projecting in response to position |

US20090310095 * | Jul 11, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods associated with projecting in response to conformation |

US20090310096 * | Jul 11, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of Delaware | Systems and methods for transmitting in response to position |

US20090310097 * | Aug 22, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Projection in response to conformation |

US20090310098 * | Aug 22, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for projecting in response to conformation |

US20090310101 * | Sep 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Projection associated methods and systems |

US20090310102 * | Sep 30, 2008 | Dec 17, 2009 | Searete Llc. | Projection associated methods and systems |

US20090310103 * | Feb 27, 2009 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for receiving information associated with the coordinated use of two or more user responsive projectors |

US20090312854 * | Feb 27, 2009 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for transmitting information associated with the coordinated use of two or more user responsive projectors |

US20090313150 * | Oct 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods associated with projection billing |

US20090313151 * | Oct 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods associated with projection system billing |

US20090313152 * | Oct 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems associated with projection billing |

US20090313153 * | Oct 30, 2008 | Dec 17, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware. | Systems associated with projection system billing |

US20090324138 * | May 12, 2009 | Dec 31, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems related to an image capture projection surface |

US20090326681 * | Jun 30, 2008 | Dec 31, 2009 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Systems and methods for projecting in response to position |

US20100002204 * | Jun 30, 2008 | Jan 7, 2010 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Motion responsive devices and systems |

US20100066689 * | Jul 2, 2009 | Mar 18, 2010 | Jung Edward K Y | Devices related to projection input surfaces |

US20100066983 * | Jul 2, 2009 | Mar 18, 2010 | Jun Edward K Y | Methods and systems related to a projection surface |

US20110007278 * | Jul 1, 2010 | Jan 13, 2011 | Thomson Licensing | Method and system for differential distortion correction for three-dimensional (3D) projection |

US20110032340 * | Jul 29, 2010 | Feb 10, 2011 | William Gibbens Redmann | Method for crosstalk correction for three-dimensional (3d) projection |

US20110038042 * | Aug 12, 2010 | Feb 17, 2011 | William Gibbens Redmann | Method and system for crosstalk and distortion corrections for three-dimensional (3D) projection |

US20110176119 * | Aug 22, 2008 | Jul 21, 2011 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Methods and systems for projecting in response to conformation |

CN102903085A * | Sep 25, 2012 | Jan 30, 2013 | 福州大学 | Rapid image mosaic method based on corner matching |

CN102903085B * | Sep 25, 2012 | Sep 9, 2015 | 福州大学 | 基于角点匹配的快速图像拼接方法 |

Classifications

U.S. Classification | 353/70 |

International Classification | G03B21/00, G03B21/14 |

Cooperative Classification | H04N9/3185, G03B21/14 |

European Classification | H04N9/31S3, G03B21/14 |

Legal Events

Date | Code | Event | Description |
---|---|---|---|

May 19, 2004 | AS | Assignment | Owner name: PIXELWORKS, INC., OREGON Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:WANG, ZHONGDE;TENG, TIANBING BRIAN;REEL/FRAME:015363/0255 Effective date: 20040430 |

Jul 29, 2009 | FPAY | Fee payment | Year of fee payment: 4 |

Mar 13, 2013 | FPAY | Fee payment | Year of fee payment: 8 |

Rotate